Barmpalias, G, Elwes, R and Lewis-Pye, A (2015) Tipping Points in 1-dimensional Schelling Models with Switching Agents. Journal of Statistical Physics, 158 (4). 806 - 852. ISSN 0022-4715
Abstract
Schelling’s spacial proximity model was an early agent-based model, illustrating how ethnic segregation can emerge, unwanted, from the actions of citizens acting according to individual local preferences. Here a 1-dimensional unperturbed variant is studied under switching agent dynamics, interpretable as being open in that agents may enter and exit the model. Following the authors’ work (Barmpalias et al., FOCS, 2014) and that of Brandt et al. (Proceedings of the 44th ACM Symposium on Theory of Computing (STOC 2012), 2012), rigorous asymptotic results are established. The dynamic allows either type to take over almost everywhere. Tipping points are identified between the regions of takeover and staticity. In a generalization of the models considered in [1] and [3], the model’s parameters comprise the initial proportions of the two types, along with independent values of the tolerance for each type. This model comprises a 1-dimensional spin-1 model with spin dependent external field, as well as providing an example of cascading behaviour within a network.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014, Springer Science+Business Media New York. This is an author produced version of a paper published in Journal of Statistical Physics. The final publication is available at Springer via http://dx.doi.org/10.1007/s10955-014-1141-5 |
Keywords: | Schelling segregation; Algorithmic game theory; Complex systems; Nonlinear dynamics; Ising model; Spin glass; Network science |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Oct 2015 10:41 |
Last Modified: | 04 Nov 2015 07:14 |
Published Version: | http://dx.doi.org/10.1007/s10955-014-1141-5 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s10955-014-1141-5 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:90282 |